SWI-Prolog -- transpose/2

?- transpose([[1,2,3],[4,5,6],[7,8,9]], Ts).
Ts = [[1, 4, 7], [2, 5, 8], [3, 6, 9]].

This predicate is useful in many constraint programs. Consider for instance Sudoku:

sudoku(Rows) :-
 length(Rows, 9), maplist(same_length(Rows), Rows),
 append(Rows, Vs), Vs ins 1..9,
 maplist(all_distinct, Rows),
 transpose(Rows, Columns),
 maplist(all_distinct, Columns),
 Rows = [As,Bs,Cs,Ds,Es,Fs,Gs,Hs,Is],
 blocks(As, Bs, Cs), blocks(Ds, Es, Fs), blocks(Gs, Hs, Is).
blocks([], [], []).
blocks([N1,N2,N3|Ns1], [N4,N5,N6|Ns2], [N7,N8,N9|Ns3]) :-
 all_distinct([N1,N2,N3,N4,N5,N6,N7,N8,N9]),
 blocks(Ns1, Ns2, Ns3).
problem(1, [[_,_,_,_,_,_,_,_,_],
 [_,_,_,_,_,3,_,8,5],
 [_,_,1,_,2,_,_,_,_],
 [_,_,_,5,_,7,_,_,_],
 [_,_,4,_,_,_,1,_,_],
 [_,9,_,_,_,_,_,_,_],
 [5,_,_,_,_,_,_,7,3],
 [_,_,2,_,1,_,_,_,_],
 [_,_,_,_,4,_,_,_,9]]).

Sample query:

?- problem(1, Rows), sudoku(Rows), maplist(portray_clause, Rows).
[9, 8, 7, 6, 5, 4, 3, 2, 1].
[2, 4, 6, 1, 7, 3, 9, 8, 5].
[3, 5, 1, 9, 2, 8, 7, 4, 6].
[1, 2, 8, 5, 3, 7, 6, 9, 4].
[6, 3, 4, 8, 9, 2, 1, 5, 7].
[7, 9, 5, 4, 6, 1, 8, 3, 2].
[5, 1, 9, 2, 8, 6, 4, 7, 3].
[4, 7, 2, 3, 1, 9, 5, 6, 8].
[8, 6, 3, 7, 4, 5, 2, 1, 9].
Rows = [[9, 8, 7, 6, 5, 4, 3, 2|...], ... , [...|...]].